Home
Class 12
MATHS
The vector hat i+x hat j+3 hat k is rot...

The vector ` hat i+x hat j+3 hat k` is rotated through an angle `theta` and doubled in magnitude, then it becomes `4 hat i+(4x-2)dot hat j+2 hat k` . Then value of `x` are (a) `-2/3` (b) `1/3` (c) `2/3` (d) 2

A

`{-(2)/(3),2}`

B

`((1)/(3),2)`

C

`{(2)/(3),0}`

D

`{2,7}`

Text Solution

Verified by Experts

The correct Answer is:
A
Since, the vector `hati+xhatj+3hatk`k is doubled in magnitude, then it becomes
`4hati+(4x-2)hatj+2hatk`
`therefore 2|hati+xhatj+3hatk|=4hati+(4x-2)hatj+2hatk|`
`implies 2sqrt(2+x^(2)+9)=sqrt(16+(4x-2)^(2)+4)`
`implies 40+4x^(2)=20+(4x-2)^(2)`
`implies 3x^(2)-4x-4=0`
`implies (x-2)(3x+2)=0`
`implies x=2,-(2)/(3)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The magnitude of the vector 6hat(i) + 2hat(j) + 3hat(k) is ?

Find the magnitude of the vector vec(a) = 3hat(i) +2hat(j) + 6hat(k) .

Find the direction cosines of vector, 2hat(i) + hat(j) + 3hat(k) .

Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Find unit vector in which the direction of vector vec a = 2 hat i + 3 hat j + hat k .

If vec A =2 hat i+ 3 hat j+ 8 hat k is perpendicular to vec B= 4 hat j -4 hat i+ alpha hat k , then the value of alpha

Write a vector of magnitude 15 units in the direction of vector hat(i) - 2hat(j) + 2hat(k) .

if vec a= 2 hat i+ lambda hat j+ hat k and vec b= hat i+ 2 hat j+ 3 hat k are orthogonal then the value of lambda